Response of nonlinear soil-MDOF structure systems subjected to distinct frequency-content components of near-fault ground motions

EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. (2013)Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.2367

Response of nonlinear soil-MDOF structure systems subjected todistinct frequency-content components of near-fault ground motions

Faramarz Khoshnoudian1, Ehsan Ahmadi1,* and Sina Sohrabi2

1Department of Civil Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran2School of Engineering, Shiraz University, Shiraz, Iran

SUMMARY

This paper is devoted to investigate the effects of near-fault ground motions on the seismic responses ofnonlinear MDOF structures considering soil-structure interaction (SSI). Attempts are made to take intoaccount the effects of different frequency-content components of near-fault records including pulse-type (PT) and high-frequency (HF) components via adopting an ensemble of 54 near-fault groundmotions. A deep sensitivity analysis is implemented based on the main parameters of the soil-structuresystem. The soil is simulated based on the Cone model concept, and the superstructure is idealized as anonlinear shear building. The results elucidate that SSI has approximately increasing and mitigatingeffects on structural responses to the PT and HF components, respectively. Also, a threshold period existsabove which the HF component governs the structural responses. As the fundamental period of the struc-ture becomes shorter and structural target ductility reduces, the contribution of the HF component to thestructural responses increases, elaborately. Soil flexibility makes the threshold period increase, and theeffect of the PT component becomes more significant than the HF one. In the case of soil-structure system,slenderizing the structure also increases this threshold period and causes the PT component to bedominant. Copyright © 2013 John Wiley & Sons, Ltd.

Received 14 January 2013; Revised 10 August 2013; Accepted 15 August 2013

KEY WORDS: near-fault ground motions; record decomposition; pulse-type and high-frequencycomponents; soil-structure interaction; multi-story structures

1. INTRODUCTION

Ground shakings in the vicinity of active faults have some notable characteristics that make themdifferent from ordinary ground motions. Fling step and forward directivity effects are the twoprominent properties of near-fault ground motions, which can significantly affect the response ofstructures. Fling step is due to static displacement arising from fault motions. Forward directivityemanates from the fault rupture when it occurs at the same velocity as the shear-wave velocity ofthe site. Between these two important effects, the forward directivity is intended to be the focused inthis study. Many studies have been carried out to investigate the salient properties of near-faultground motions with forward directivity effects [1–3]. Somerville (2000) made attempt to shed lighton the particular effects of forward directivity [4]. Mavroeidis and Papageorgiou (2002, 2003)investigated characteristics of near-fault ground motions and suggested an expression to replicate thepulse-type (PT) component of near-fault ground motions [5, 6]. Mavroeidis et al. (2004) elucidatedthat such pulses are capable to significantly affect their corresponding spectrum [7]. Hubbard and

* Correspondence to: Ehsan Ahmadi, Department of Civil Engineering, Amirkabir University of Technology (TehranPolytechnic), Tehran, Iran.†E-mail: [email protected]

Copyright © 2013 John Wiley & Sons, Ltd.

F. KHOSHNOUDIAN, E. AHMADI AND S. SOHRABI

Mavroeidis (2011) stated that forward directivity pulses can considerably influence the dampingmodification factors [8]. Tang and Zhang (2011) proposed an approach to recognize the PTcomponent available in near-fault ground motions [9]. Iervolino et al. (2012) investigated theinelastic displacement factors under near-fault ground motions and suggested a formulation forcalculating inelastic displacement ratios [10]. As well, near-fault ground motions cansignificantly affect the response of structures [11–14]. Alavi and Krawinkler (2004) studied theresponses of multi-story frame structures subjected to both near-fault and ordinary groundmotions, and it was found that near-fault ground motions are capable to enforce higher demandsto the structures [15]. Kalkan and Kunnath (2006) concluded that higher stories experiencehigher demands than lower ones due to the both forward and fling step pulses [16]. Sehhati et al.(2011) investigated the story ductility distribution over the structure height under ordinary andnear-fault ground motions and inferred that upper stories undergo greater demands than lowerones for near-fault ground motions [17]. All the previous studies were carried out for fixed-basestructures, and there were no trace of soil flexibility.

Researchers made attempt to decompose the near-fault record through different approaches. Baker(2007) employed wavelet analysis to separate the PT and high-frequency (HF) parts of near-faultrecords. The HF part was the difference between the original record and the extracted PTcomponent and was quoted as the residual record in Baker’s study [18]. Xu and Agrawal (2010)adopted empirical mode decomposition to segregate the dominant PT and HF components of near-fault ground motions [19]. Ghahari et al. (2010) utilized a moving average filtering with anappropriate cut-off frequency to decompose the near-fault record. In their investigation, the PTand HF parts of the record were quoted as pulse-type record and background record, respectively[20]. Besides the PT component of the near-fault ground motion, the HF component of the near-fault record might considerably affect the structural responses. Significance of the HF part wasalso noted by other researchers [4–7, 21–23]. Somerville (2000) demonstrated that accelerationresponse spectra of near-fault records for moderate-to-large earthquakes are stronger than thoseobtained for very large earthquakes in the HF range [4]. Similar results also were observed byMavroeidis and Papageorgiou (2002, 2003) [5, 6]. Mavroeidis et al. (2004) verified that strongerearthquakes exhibit rich contents in low frequency ranges (PT ranges), whereas the smallerearthquakes are specified by the HF components [7]. It should be noted that the aforementionedstudies have focused on the seismological aspects of near-fault records. Ghobarah (2004)investigated engineering aspect of the HF component and revealed that the HF portion of the near-fault record can be important, particularly for short-period structures [21]. He investigated onlynear-fault ground motions with long-period pulses and concluded that long-period pulses mayaffect fundamental mode of structures, and the HF component may comply with the higher modesleading to significant total response for structures. Elsheikh and Ghobarah (2004) verified that HFcontent of the near-fault record can influence the demands of stiff structures [23]. However, thesestudies did not address a definite pattern for domination of each component (PT and HF). As well,the number of records was not sufficient to conclude general results. From this view, acomprehensive study is required to capture characteristics of both components. Also, all studieshave been performed on fixed-base structures, and hence, soil-structure interaction (SSI) effectshave been disregarded.

On the other hand, SSI mechanism significantly impresses dynamic properties of the superstructure.Elastic demands of structures were evaluated by many researchers considering SSI effects [24–26].Nonlinear response of soil-structure system was also scrutinized [27–31]. Ductility and strengthdemands of structures experience notable changes due to the SSI effects [31]. Also, it wasdemonstrated that hysteretic energy dissipated due to the structure is affected by interactionphenomenon during strong earthquakes [32]. Aviles and Perez-Rocha (2003, 2005) made attempt tocombine the SSI effects with the nonlinear behavior of the structure through modifying strengthreduction factors [30, 33]. Aviles and Perez-Rocha (2011) proposed a new technique to obtaindisplacement demand associated with strain in the superstructure by removing rigid body motions ofthe foundation from global displacement of the soil-structure system [34]. It was shown that SSIeffects also can change the damage index of buildings [35, 36]. Although the demands of soil-structure systems have been investigated under ordinary ground motions, the effects of different

Copyright © 2013 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. (2013)DOI: 10.1002/eqe

SOIL-STRUCTURE INTERACTION

portions of near-fault ground motions, particularly PT and HF components, have been ignored.Recently, Khoshnoudian and Ahmadi studied the effects of pulse period on the demands of soil-structure systems using simplified pulses. Response of soil-structure systems primarily depends onthe pulse-to-interacting system period ratio instead of pulse-to-fixed-base structure period ratio.Also, higher-mode effects are more significant when considering SSI effects [37]. However,simplified pulses have been used in their study, and the HF component has been disregarded.Therefore, it is necessary to investigate the influence of the HF component in a follow-up study.

As previously noted, soil-structure mechanism and different portions of near-fault ground motionscan extremely affect the structural responses. Also, there is lack of knowledge in the case of the HFcomponent effects on the structural demands for both fixed-base structures and soil-structuresystems. Therefore, the primary goal of this study is to elucidate the impacts of two distinctcomponents of near-fault record, that is. PT and HF parts, on the demands of multi-story structureswith and without including SSI effects and to clarify what component renders higher demands to thesystem studied. Such issue has not been addressed so far not only for fixed-base structure but alsofor soil-structure systems. A suite of 54 original near-fault records and their correspondingcomponents extracted by Baker are adopted [18]. Nondimensional frequency, aspect ratio of thesuperstructure, and structural target ductility are selected as the main parameters of the soil-structuresystem. First, the importance of higher-mode effects is clearly identified using replacement SDOFoscillator approach. Then, a deep sensitivity analysis is conducted to detect the influences of variouswell known components of near-fault ground motions and interacting parameters on responses ofnonlinear soil-MDOF structure systems. To this end, three different response indicators areintroduced to respectively investigate SSI effects on each component of the original records, relativeeffects of the HF component to the PT one, and more importantly variations of each componentrelative to the original record.

2. SOIL-STRUCTURE MODEL, GOVERNING INTERACTING PARAMETERS, ANDVERTICAL DISTRIBUTION OF STIFFNESS AND STRENGTH

The soil-structure system assumed herein, shown in Figure 1, is similar to the model used by theauthors in their previous paper [37]. The entire system contains a multi-story structure resting onthe surface of the soil. The MDOF superstructure and soil are simulated as nonlinear shearbuilding and Cone model [38–41], respectively. The horizontal, s, (sway) and the rocking, ϕ,DOFs are introduced as the translational and rotational motions of the foundation, respectively.Also, the additional internal DOF, θ, is used to consider the frequency-dependent soil stiffness. usand ϕhn indicate the horizontal displacement components caused by the sway and rockingmotions at the roof story. un represents the deformation that is associated with the strain in thesuperstructure. Note that only the inertial part of the SSI is considered in this paper. In otherwords, the kinematic part of the SSI is ignored assuming the rigid foundation to lie on the surfaceof the soil with no embedment and subjected to vertically incident plane shear waves with particlemotion in the horizontal direction. However, particular attention should be placed on the fact thatthe kinematic effects can reduce the translational motion (filtering of the HF component) andgenerate a rocking motion. The consequences may be important for tall buildings, which are moreeffectively excited by the induced rocking motion, and also for low-rise buildings excited by thereduced translational motion.

As the authors concluded in their previous study [37], SSI effects lead to amplify higher-modeeffects, particularly under forward directivity pulses. Also, in the following, numerical results on theimportance of higher-mode effects are presented (Section 4). Therefore, higher-mode effects are alsoimportant and should be taken into account and a SDOF oscillator with different natural periodscannot capture the nature of pulse-like ground motions. The simplified structure model used by theauthors is based on the structural modeling explained by Federal Emergency Management Agency(FEMA) 440 [42]. On the basis of FEMA 440 (chapter 2), in some cases (e.g. shear beam or strongbeam-to-weak column frames), engineers can simplify complex structural models into equivalentMDOF models, which are called stick models. In the paper, the stick model of shear beam is used.


Figure 1. Flexible-base system.


Also, lateral stiffness and yielding strength over the structure height are distributed nonuniformly. Tothis end, the vertical distribution factor is computed as suggested by ASCE/SEI 7–10 standard [43].Thus, the story shear at any level (ith story) can be determined from the following equation:

Vi ¼ CviVb ¼ wihki =∑

nj¼1wjh

kj

� �Vb (1)

Cvi and Vb stand for vertical distribution factor and base shear, respectively. wi and wj denote theportion of total effective weight of the structure assigned to the level i and j, respectively. hi and hjrepresent the height from the structure base to the level i and j, correspondingly. k indicates anexponent related to the structure period taking value of 1 for structures with a period of 0.5 s or less,2 for structures having a period of 2.5 s or more, and a linear interpolation is required for structureswith periods between 0.5 and 2.5 s.

Vertical distribution of the stiffness and yielding strength is based on the vertical distribution factor,Cvi. Accordingly, the stiffness and yielding strength at any level (ith story) can be calculated using thefollowing equations:

ki ¼ Cvikb (2)

Vyi ¼ CviVyb (3)



kb is the stiffness associated with the base story, which is computed so that the natural period of thefixed-base structure be the same as the specified period. It should be noted that 5-story, 15-story,and 25-story buildings are assumed for superstructure with respective fundamental fixed-baseperiods of 0.7, 1.5, and 2.3 s. Vyb is the yielding strength corresponding to the base story that can beobtained from an iterative procedure in order to reach the specified structural target ductility.Therefore, attempts are made to distribute the stiffness and strength along the height of the structurebased on the ASCE/SEI 7–10 standard so that it approximately complies with the stiffness andstrength distribution in real structures. Detailed information about the structural modeling and soilsimulations can be found in Khoshnoudian and Ahmadi’s study [37].

It is well known that effects of structural size, modal characteristics of the superstructure, and thesoil attributes can be best considered by the three parameters of nondimensional frequency, aspectratio and structural target ductility [26, 44]. In order to include soil flexibility in the studiedsystems, nondimensional frequency, a0, is defined as an indicator for the structure-to-soil stiffnessratio, ωfixhn/Vs, where ωfix, hn, and Vs are circular frequencies of the fixed-base structure, totalheight of the superstructure, and shear-wave velocity, respectively. This indicator can have valuesof up to 3 for conventional buildings located on very soft soil and values very close to zero arerepresentatives of the fixed-base structures. In this study, this parameter is assumed to be 0, 1, 2,and 3. The aspect ratio, which shows slenderness of the superstructure, is defined as the ratio oftotal height of the superstructure to the foundation radius, that is, hn/r. In this paper, values of 1,2, 3, and 4 are assigned to this parameter to include a wide range of aspect ratios. Nonlinearitylevel in the superstructure is controlled by structural target ductility, μ, assuming 2, 4, and 8.These three factors are commonly selected as the key parameters of the system [26, 44].

The n + 3-DOF soil–structure model, where n is number of stories, used herein has the capability tobe analyzed in the time domain. To this end, MATLAB program is developed to analyze the soil-structure systems [45]. First, the yielding base shear of the superstructure is calculated by iterationin order to reach the specified structural target ductility in the soil-MDOF structure system withinaccuracy of 1% under the selected acceleration time history. Herein, the model is analyzed by usingβeta Newmark method with modified Newton–Raphson approach. The modified Newton–Raphsontechnique expedites the convergence using the tangent stiffness matrix. Accordingly, demands of allstories are calculated for the fixed-base structures as well as the soil-structure systems.

3. GROUND MOTION DATABASE

The ground motion database assembled for nonlinear time history analyses of the soil-structuresystems consists of an extensive representative ensemble of near-fault ground motions. A total of 54ground motions from 15 earthquakes are chosen from Next Generation Attenuation ground motionlibrary (http://peer.berkeley.edu/nga). This ground motion suit is a subset of the records used byBaker [18] and related to soil type D and E. Figure 2 illustrates acceleration and velocity spectrawith 5% damping ratio for original and decomposed components of the record E12 (Table I).

Figure 2. Acceleration and velocity spectra with 5% damping ratio for original and decomposed componentsof the record E12.


http://peer.berkeley.edu/nga

Table I. List of near-fault ground motions used in this study.

Label Event Year Station Tp PGV (cm/s) Mw Epi. D. Soil Type

E1 Imperial Valley-06 1979 Aeropuerto Mexicali 2.4 44.3 6.5 2.5 DE2 Imperial Valley-06 1979 Agrarias 2.3 54.4 6.5 2.6 DE3 Imperial Valley-06 1979 Brawley Airport 4.0 36.1 6.5 43.2 DE4 Imperial Valley-06 1979 EC County Center FF 4.5 54.5 6.5 29.1 EE5 Imperial Valley-06 1979 EC Meloland Overpass FF 3.3 115.0 6.5 19.4 DE6 Imperial Valley-06 1979 El Centro Array #10 4.5 46.9 6.5 26.3 DE7 Imperial Valley-06 1979 El Centro Array #11 7.4 41.1 6.5 29.4 DE8 Imperial Valley-06 1979 El Centro Array #3 5.2 41.1 6.5 28.7 EE9 Imperial Valley-06 1979 El Centro Array #4 4.6 77.9 6.5 27.1 DE10 Imperial Valley-06 1979 El Centro Array #5 4.0 91.5 6.5 27.8 DE11 Imperial Valley-06 1979 El Centro Array #6 3.8 111.9 6.5 27.5 DE12 Imperial Valley-06 1979 El Centro Array #7 4.2 108.8 6.5 27.6 DE13 Imperial Valley-06 1979 El Centro Array #8 5.4 48.6 6.5 28.1 DE14 Imperial Valley-06 1979 El Centro Differential Array 5.9 59.6 6.5 27.2 DE15 Imperial Valley-06 1979 Holtville Post Office 4.8 55.1 6.5 19.8 DE16 Irpinia, Italy-01 1980 Sturno 3.1 41.5 6.9 30.4 DE17 Westmorland 1981 Parachute Test Site 3.6 35.8 5.9 20.5 DE18 Coalinga-07 1983 Coalinga-14th & Elm

(Old CHP)0.4 36.1 5.2 9.6 D

E19 Taiwan SMART1(40) 1986 SMART1 C00 1.6 31.2 6.3 68.2 DE20 Taiwan SMART1(40) 1986 SMART1 M07 1.6 36.1 6.3 67.2 DE21 N. Palm Springs 1986 North Palm Springs 1.4 73.6 6.1 10.6 DE22 Whittier Narrows-01 1987 Downey - Co Maint Bldg 0.8 30.4 6.0 16.0 DE23 Whittier Narrows-01 1987 LB - Orange Ave 1.0 32.9 6.0 20.7 DE24 Superstition Hills-02 1987 Parachute Test Site 2.3 106.8 6.5 16.0 DE25 Loma Prieta 1989 Alameda Naval

Air Stn Hanger2.0 32.2 6.9 90.8 E

E26 Loma Prieta 1989 Gilroy Array #2 1.7 45.7 6.9 29.8 DE27 Loma Prieta 1989 Oakland - Outer

Harbor Wharf1.8 49.2 6.9 94.0 D

E28 Erzican, Turkey 1992 Erzincan 2.7 95.4 6.7 9.0 DE29 Landers 1992 Barstow 8.9 30.4 7.3 94.8 DE30 Landers 1992 Yermo Fire Station 7.5 53.2 7.3 86.0 DE31 Northridge-01 1994 LA - Wadsworth

VA Hospital North2.4 32.4 6.7 19.6 D

E32 Northridge-01 1994 Sylmar - Converter Sta 3.5 130.3 6.7 13.1 DE33 Northridge-01 1994 Sylmar - Converter Sta East 3.5 116.6 6.7 13.6 DE34 Northridge-01 1994 Sylmar - Olive View

Med FF3.1 122.7 6.7 16.8 D

E35 Kobe, Japan 1995 Takarazuka 1.4 72.6 6.9 38.6 EE36 Kobe, Japan 1995 Takatori 1.6 169.6 6.9 13.1 EE37 Chi-Chi, Taiwan 1999 CHY006 2.6 64.7 7.6 40.5 DE38 Chi-Chi, Taiwan 1999 CHY035 1.4 42.0 7.6 43.9 DE39 Chi-Chi, Taiwan 1999 CHY101 4.8 85.4 7.6 32.0 DE40 Chi-Chi, Taiwan 1999 TAP003 3.4 33.0 7.6 151.7 EE41 Chi-Chi, Taiwan 1999 TCU031 6.2 59.9 7.6 80.1 DE42 Chi-Chi, Taiwan 1999 TCU036 5.4 62.4 7.6 67.8 DE43 Chi-Chi, Taiwan 1999 TCU038 7.0 50.9 7.6 73.1 DE44 Chi-Chi, Taiwan 1999 TCU040 6.3 53.0 7.6 69.0 EE45 Chi-Chi, Taiwan 1999 TCU065 5.7 127.7 7.6 26.7 DE46 Chi-Chi, Taiwan 1999 TCU075 5.1 88.4 7.6 20.7 DE47 Chi-Chi, Taiwan 1999 TCU076 4.0 63.7 7.6 16.0 DE48 Chi-Chi, Taiwan 1999 TCU098 7.5 32.7 7.6 99.7 DE49 Chi-Chi, Taiwan 1999 TCU103 8.3 62.2 7.6 52.4 DE50 Northwest China-03 1997 Jiashi 1.3 37.0 6.1 19.1 DE51 Yountville 2000 Napa Fire Station #3 0.7 43.0 5.0 9.9 DE52 Chi-Chi, Taiwan-03 1999 CHY024 3.2 33.1 6.2 25.5 DE53 Chi-Chi, Taiwan-03 1999 TCU076 0.9 59.4 6.2 20.8 DE54 Chi-Chi, Taiwan-06 1999 CHY101 2.8 36.3 6.3 50.0 D




A complete list of the original records and their characteristics such as pulse period (Tp), peakground velocity, and epicentral distance are presented in Table I. Baker developed a procedure toextract the largest velocity pulse from a record. The procedure consists of using the wavelettransform to identify the dominant pulse of the record. Baker used the size of the extracted pulserelative to the original ground motion to develop a quantitative criterion for classifying a groundmotion as pulse-like. To identify the pulse-like records potentially caused by directivity effects, twoadditional criteria were applied: the pulse arrives at the beginning of the strong ground motion, andthe absolute amplitude of the velocity pulse is large relative to the remainder of the record.

4. THE IMPORTANCE OF HIGHER-MODE EFFECTS FOR SOIL-STRUCTURE SYSTEMS

Before response indicators are evaluated under various components of near-fault ground motions, it isdesired to clearly identify the influence of SSI on higher modes. To this end, the response of the MDOFsystems is compared with that obtained from a replacement SDOF oscillator. This nonlinear modal

oscillator [34] is characterized by the effective mass, M ¼ ∑ni¼1miϕi

� �2=∑n

i¼1miϕ2i , and height, H ¼

∑ni¼1miϕihi=∑

ni¼1miϕi, corresponding to the fundamental vibration mode of the fixed-base structure,

as well as by the effective period, eT , damping, eζ , and ductility, eμ, of the soil-structure system:

eT ¼ T

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k

ks1þ h2n

kskφ

� �s(4)

eζ ¼ TeT� �3

ζ s þ ζ f (5)

eμ ¼ 1þ μ� 1ð Þ T2

eT2 (6)

ζs and ζf represent viscous damping of superstructure and foundation damping, respectively.Foundation damping is obtained as addressed in FEMA 440 [42]. T stands for fundamentalperiod of fixed-base SDOF oscillator. Also, k denotes the stiffness of fixed-base SDOFoscillator, M(2π/T)2. The difference between the responses of both the MDOF system and thereplacement SDOF oscillator reflects the higher-mode effects. Herein, the ratio of roofdisplacements of the MDOF system and the replacement SDOF oscillator, βm, is considered toidentify higher-mode effects. Figure 3 illustrates βm-values of the 5-story and 25-story modelswith structural ductility of 4 for both fixed-base structure (a0 = 0) and flexible-base system(a0 = 3, hn/r = 4). As it can be seen, SSI effects increase higher-mode effects for both PT and HFcomponents. Moreover, as the pulse period elongates, βm-values for HF component becomegreater than the corresponding values for PT component. It should be noted that the results holdfor other cases not shown herein.

5. RESPONSE OF SOIL-MDOF STRUCTURE SYSTEMS TO SEPARATE COMPONENTS OFNEAR-FAULT GROUND MOTIONS

In this part, it is intended to compare the effects of the PT and HF components of near-fault groundmotions on the seismic behavior of the fixed-base structures and interacting systems. The groundmotion database described in Section 3 and the soil-structure system introduced in the Section 2 areadopted to conduct a deep nonlinear time history analysis. Three different series of analysis areperformed for original records and their corresponding PT and HF components. Maximum interstorydrift ratio (MIDR) among all stories is selected as Engineering demand parameter. Interstory drift


Figure 3. βm-values of the 5-story and 25-story models with structural ductility of 4 for both (a) fixed-basesystem (a0 = 0) (b) flexible-base system (a0 = 3, hn/r = 4).


ratio for each story is described as the relative displacements between two consecutive storiesnormalized by the story height. Displacement demands like MIDR are useful for displacement-baseddesign procedures [15–17]. Therefore, the authors intend to evaluate displacement demands andtrack the quota of the both PT and HF components. To measure the contributions of the PT and HFcomponents of original records (OR), three indicators are defined, as follows:

(1) To investigate the SSI effects on each component separately, the displacement demand ratios PT(a0)/PT(0) and HF(a0)/HF(0) are calculated for the PT and HF components, respectively.

(2) To investigate the relative effects of the PT and HF components, displacement demand ratios PT(a0)/HF(a0) and PT(0)/HF(0) are computed for flexible-base and fixed-base systems, respectively.

(3) To measure the contributions of the PT and HF components of OR, the parameters RD =MIDR(PT)/MIDR(OR) and RD=MIDR(HF)/MIDR(OR), with MIDR being the maximum interstorydrift ratio among all stories, are determined for flexible- and fixed-base systems, respectively.This ratio also specifies which component of the original record is predominant in determinationof the system.

In other words, these three indicators quantify the effects of the PT and HF parts and make itpossible to compare these two prominent components, elaborately. In the following, for all graphs,the horizontal axis shows the pulse period extracted by wavelet analysis [18]. In the previousstudies like [10, 15–17], it has been confirmed that pulse period (Tp) is expected to be the mostimportant feature of this kind of ground motions. Additionally, it should be noted that for the sakeof brevity all graphs are skipped to be presented for all values of nondimensional frequencies andaspect ratios. Herein, to draw main conclusions, only values corresponding to extreme conditions,that is, values of 0 (fixed-base structure), and 3 (dominant SSI effects) for nondimensionalfrequency, and values of 1 (squatty structure) and 4 (slender structure) for aspect ratio arerepresented. However, the results hold for other values of nondimensional frequency and aspectratio not shown here.

5.1. Displacement demand ratios PT(a0)/PT(0) and HF(a0)/HF(0)

Displacement demand ratios, PT(a0)/PT(0) and HF(a0)/HF(0), are illustrated in Figures 4 and 5 for the5-story and 25-story buildings, respectively, assuming nondimensional frequency of 3 and aspect ratio


Figure 4. Displacement demand ratios PT(a0)/PT(0) and HF(a0)/HF(0) of the 5-story model for PT and HFcomponents, respectively.

Figure 5. Displacement demand ratios PT(a0)/PT(0) and HF(a0)/HF(0) of the 25-story model for PT and HFcomponents, respectively.


of 1 and 4 to investigate the effects of SSI on different components of original records. For all cases,either the PT component or HF component, the displacement demand ratios are greater for the slenderstructures than those obtained from the squatty structures. This can be justified by the fact that waveradiation in the soil is more influential for squatty structures [44].

Another worth mentioning point is that this ratio becomes larger than one in some cases for the PTcomponent, while it is smaller than one for the HF component in the most cases. SSI influences havemitigating effects on structural demands because of the radiation and hysteretic (material) damping inthe soil as it is seen here for the HF component. However, for the PT component, the situation differs



from the HF component, and it seems that the stiffness reduction of the system due to the soil-flexibility is governing in some cases and can cause the structural responses to be more than itscorresponding fixed-base structure.

Generally, SSI can influence structural responses through two main sources. The first one is through soildamping that consists of radiation and material damping. These two types of damping arising from the soilcan reduce the responses in comparison with the fixed-base structure. The second one is soil flexibility thatmakes the total stiffness of the system decrease. Reduction in the system’s stiffness can have increasingeffects on the system demands. Therefore, there is a competition between these two sources to determinethe response of the system. It seems that in the case of the HF component, soil damping is governingand controlling the total response, while it is the soil flexibility, which is dominant for the PTcomponent and may increase structural demands by reducing overall stiffness of the system. Increasingstructural ductility can amplify this phenomenon because structural yielding can affect the gain ofdamping because of radiation and makes radiation damping decrease [27, 28]. As Figures 4 and 5illustrate, values of displacement demand ratios tend to approach 1 and more for higher structural ductility.

5.2. Displacement demand ratios PT(a0)/ HF(a0) and PT(0)/ HF(0)

In this section, attempts are made to investigate the relative trend of the PT and HF components oforiginal records. Figure 6 represents displacement demand ratios, that is, PT(a0)/HF(a0) and PT(0)/HF(0), for the flexible- (a0 = 3 and hn/r = 4) and fixed-base systems, respectively, versus pulse

Figure 6. Displacement demand ratios PT(a0)/HF(a0) and PT(0)/HF(0) for flexible- (a0 = 3 and hn/r = 4) andfixed-base systems, respectively.



period. At very short-period pulses, this ratio is the most significant for the low structural ductility. But,as the pulse period increases, this ratio reduces for the low structural ductility and increases for higherstructural ductility. In other words, the plots move toward the right side of the pulse period axis withincreasing structural ductility due to the period elongation caused by structural yielding.

The black dash line corresponds to the ratio of 1. When the plot is above the black dash line, itmeans that the quota of the PT component in the structural response is larger than the HFcomponent. The graphs have nearly a descending pattern with respect to the pulse period. It impliesthat as the pulse period elongates, the values of demands associated with the PT componentdecreases, and the corresponding values relevant to the HF component augments.

The intersection point of the black dash line and plots specifies a pulse period above which theinfluence of the HF component is dominant. Comparing the graphs on the left and right side of theFigure 6 indicates the effects of SSI on the intersection point. This intersection point shifts towardthe right side of the graph because of the period of elongation generated by SSI effects.

In addition, increasing structural target ductility has the same effect as the SSI on the intersectionpoint. To interpret this intersection point more clearly and see the variation trend of each componentseparately, in the next section, ratio of demands associated with each component, that is, PT andHF, to those obtained from the original records (OR) are calculated and explained comprehensively.

5.3. Maximum interstoy drift ratios RD(a0) and RD(0)

Figure 7 illustrates variations of RD parameter for the 5-story, 15-story, and 25-story fixed-basestructure with structural target ductility of 2, 4, and 8.The PT and HF plots approximately havedescending and ascending trends, and increasing pulse period leads to decrease and increase ofthe RD parameter for the PT and HF components, respectively. It implies that the quota of the PTcomponent in the response of the structure is higher for short-period pulses, whereas the HFcomponent is predominant for long-period pulses. The reason might lie in activating higher modes

Figure 7. Variations of the RD parameter for the 5-story, 15-story, and 25-story fixed-base structures withstructural target ductility of 2, 4, and 8.



of the structure for short-period pulses. Short-period pulses are able to trigger higher modes of thestructure, and the response can be considerable for the PT component, while as the pulse periodelongates, the higher-mode effects due to the PT component decreases, and the contribution of theHF component to the response of the structure becomes significant (Figure 3). Ground motions withlong-period pulses contain the HF components that may conform to the higher modes of thestructure and result in the more significant responses. In addition to the activation of higher modesfor short-period pulses, acceleration pulses of moderate earthquakes (shorter pulses) have higheramplitudes than acceleration pulses of stronger earthquakes (longer pulses) [6, 7]. Thus, for near-fault ground motions, the PT component always is not governing, and the HF part of the motion canbe significant for ground motions with long-period pulses. Figure 7 also confirms that increasingstory numbers leads to increase and decrease of the effects of the PT and HF components onstructural demands, respectively. Therefore, as the fundamental period of the structure elongates,role of the HF component in the responses reduces and contribution of the PT portion amplifies.This conclusion is in accordance with the Ghobarah’s study, which showed that the HF partbecomes important for short-period (stiff) structures [21]. It can arise from the fact that increasingnumber of stories provides a better situation for higher modes to be activated by the PT component.From another aspect, as it is evident from Figure 2, both acceleration and velocity amplitudesare greater for the HF portion in comparison with the PT component at the short-period region ofthe spectra, and these values becomes more significant for the PT component compared to the HFone at the long-period region of the spectra.

Increasing structural target ductility causes the effects of the PT part to be meaningful. As thestructure yields, its effective period increases. In this case, higher modes do not contributesignificantly to the response due to the period elongation of the structure. In such a case,fundamental mode is the predominant mode. In some cases, values greater than 1 are reported forthe RD parameter, particularly for the PT component. It means that the response for the PT portionof the record is greater than the original record. It emanates from the phase difference between thePT and HF parts of the original record. Such difference may reduce the responses in some cases andincreases them at other cases. Comparing plots related to the PT and HF components reflects anobvious trade-off between the PT and HF portions. It means that reduction in one component isaccompanied by increase of the other component.

Also, there is a distinctive pulse period below, which the PT component is controlling. This pulseperiod corresponds to the intersection point at which the relative ratio of the PT and HF componentscoincide with the black dash line of value 1 (Figure 6). This threshold pulse period is affecteddrastically by the value of structural target ductility ratio. Increasing structural target ductilityresults in the threshold period elongation. For example, as it is obvious from Figure 7, in the caseof the 5-story building, this period complies with 1.6, 2.3, and 2.7 s for structural target ductilityof 2, 4, and 8, respectively. This can be explained by increasing effective period of the structurebecause of the increase of structural target ductility. Increasing the number of stories causes thethreshold period to increase. It means that as the structure becomes taller, the effect of the PTcomponent on the structural demand becomes more meaningful than the HF component. Thethreshold period reaches about 2.7, 3.3, and 5.2 s for the 15-story structure with structural targetductility ratios of 2, 4, and 8, respectively. Such a threshold period corresponds to 3.5, 4.2, and5.9 s for the 25-story structure. This conclusion is drawn that the HF component is predominantfor short-period structures, that is, the 5-story structure here, and its effect decreases forintermediate- and long-period structures, that is, the 15-story and the 25-story structures herein.Thus, the prevalent significant effects of the PT component for near-fault record are not valid forall pulse periods and structures. In other words, short-period structures under motions with long-period pulses can be affected more significantly by the HF part of the near-fault ground motionsthan the PT portion.

To estimate the effects of the flexible soil beneath the structure, all the plots are depicted fornondimensional frequency of 3 and aspect ratio of 4 in Figure 8. Similar to the fixed-base structures,graphs have trends downward and upward for the PT and HF portions, respectively. Also, a definitetrade-off is evident like the fixed-base case. Comparing Figures 7 and 8 sheds light on the role ofthe flexible soil in the value of the RD parameter. As it is evident from Figure 8, the trend of the


Figure 8. Variations of the RD parameter for the 5-story, 15-story, and 25-story soil-structure system(a0 = 3, hn/r =4) with structural target ductility of 2, 4, and 8.


plots is similar to the fixed-base structures, and there is a threshold period above which the HFcomponent governs the structural response. However, in the case of the soil-structure system, thevalue of threshold period is longer than those obtained from the fixed-base structures. The reasonlies in the period elongation due to the SSI effects. Period of soil-structure system is greater thanthe fixed-base structure because of the stiffness reduction of the soil-structure system. This periodelongation leads the threshold period to shift to the right side. Soil flexibility makes the thresholdperiod to reach 2.4, 4.5, and 5.2 s for the 5-story, 15-story, and 25-story structures, respectively,with structural target ductility of 2. It implies that considering SSI effects makes the PTcomponent of the near-fault ground motion to be more pronounced than the HF component. Itindirectly suggests that higher-mode effects are more significant as the soil becomes softer, andinteraction phenomenon is included (Figure 3) [37]. This phenomenon becomes more evident, asthe story number increases, and a better situation is provided for triggering higher modes. Theeffects of SSI on the threshold period become more meaningful when the structural target ductilityincreases. In this case, effective period of the system elongates as the superstructure yields, andthreshold period migrates toward higher values. The threshold period complies with the values of4, 5.9, and 7.4 s for the 5-story, 15-story, and 25-story structures with structural target ductility of8. Therefore, this conclusion is drawn that SSI effects result in the domination of the PTcomponent of near-fault ground motions. The situation is the most critical for tall buildings withhigher structural target ductility.

Although radiation damping of the soil considerably lowers the demands of the superstructure, theratio of the demands produced by the PT or HF portion to those obtained from the original record,that is RD, is not impressed by radiation damping, and the competition between the PT and HFcomponents primarily is controlled by period elongation. In other words, the effects of the SSI onthreshold period arise from the period elongation due to the reduction of the overall systemstiffness instead of radiation damping.


Figure 9. Variations of the RD parameter for the 5-story, 15-story, and 25-story soil-structure system(a0 = 3, hn/r = 1) with structural target ductility of 2, 4, and 8.


Another important key parameter, which influences the response of the soil-structure system, isaspect ratio. Figure 9 illustrates the variations of the RD parameter for the 5-story, 15-story, and25-story structures for nondimensional frequency of 3 and aspect ratio of 1. Comparing Figure 8to Figure 9 elucidates the effects of aspect ratio on the quota of various components of near-faultground motions. As the structure becomes squattier, the effects of the HF portion of near-faultground motion increases. It complies with the fact that higher modes are less activated by thePT component for squatty structures, and the fundamental mode is the mode which contributeshighly to the structural response. In the case of the squatty structures, the period elongation due toSSI effect decreases in comparison with the slender structures. This causes the threshold period todecrease so that it reaches 2.1, 3.3, and 4.2 s for the 5-story, 15-story, and 25-story structures withstructural target ductility of 2, respectively. Also, the effect of structural ductility on the increasingthreshold period is less in squatty structures compared to slender structures.

6. CONCLUSIONS

This paper attempts to address the effects of various frequency-content components of near-faultground motions on the seismic demands of multi-story structures considering SSI effects. For thispurpose, a suite of 54 near-fault records and the corresponding PT and HF components are selectedto be used in nonlinear time history analyses. The soil is simulated adopting Cone model. Thesuperstructure is idealized by an n-story nonlinear building employing stick model. Three indicatorsare defined to investigate different effects of the PT and HF components.

The results confirm that SSI has increasing and mitigating effects on the demands of the structuresfor the PT and HF components, respectively. Also, for short-period structures, the effects of the HFcomponent are the most, and as the fundamental periods of the structures elongate, the effects of theHF component mitigate, and the effects of the PT component amplify. Moreover, increasing



structural target ductility makes the PT component to be predominant due to the increase of theeffective period of the overall system. SSI effects cause the domination of the PT component andreduce the effects of the HF part. In the case of soil-structure system, increasing aspect ratio leads toreduction of the HF contribution and amplification of the PT component role. As the pulse periodincreases, the quota of the PT component decreases, and the quota associated with the HF partincreases. Therefore, a trade-off is revealed between the two components.

The shapes of the plots pertaining to RD parameter give a threshold pulse period above which theeffects of the HF portion are outstanding. This threshold pulse period is significantly affected by theSSI effects. Increasing nondimensional frequency results in the threshold pulse period elongationdue to the period elongation of the soil-structure system. Similarly, increasing aspect ratio alsocauses the threshold pulse period to increase. Also, when the structural target ductility increases, thementioned threshold period elongates.

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Response of nonlinear soil-MDOF structure systems subjected to distinct frequency-content components of near-fault ground motions